ACM Transactions on Programming Languages and Systems (TOPLAS)
Immediate atomic snapshots and fast renaming
PODC '93 Proceedings of the twelfth annual ACM symposium on Principles of distributed computing
Generalized FLP impossibility result for t-resilient asynchronous computations
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
More choices allow more faults: set consensus problems in totally asynchronous systems
Information and Computation
Set consensus using arbitrary objects (preliminary version)
PODC '94 Proceedings of the thirteenth annual ACM symposium on Principles of distributed computing
Impossibility of distributed consensus with one faulty process
Journal of the ACM (JACM)
Three-Processor Tasks Are Undecidable
SIAM Journal on Computing
The topological structure of asynchronous computability
Journal of the ACM (JACM)
Wait-Free k-Set Agreement is Impossible: The Topology of Public Knowledge
SIAM Journal on Computing
Distributed computing: fundamentals, simulations and advanced topics
Distributed computing: fundamentals, simulations and advanced topics
The Combinatorial Structure of Wait-Free Solvable Tasks
SIAM Journal on Computing
A classification of wait-free loop agreement tasks
Theoretical Computer Science - Special issue: Distributed computing
Mathematical Structures in Computer Science
Toward a Topological Characterization of Asynchronous Complexity
SIAM Journal on Computing
New combinatorial topology upper and lower bounds for renaming
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Subconsensus tasks: renaming is weaker than set agreement
DISC'06 Proceedings of the 20th international conference on Distributed Computing
Counting-based impossibility proofs for renaming and set agreement
DISC'12 Proceedings of the 26th international conference on Distributed Computing
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In the k-set agreement task each process proposes a value, and it is required that each correct process has to decide a value which was proposed and at most k distinct values must be decided. Using topological arguments it has been proved that k-set agreement is unsolvable in the asynchronous wait-free read/write shared memory model, when k n, the number of processes. This paper presents a simple, non-topological impossibility proof of k-set agreement. The proof depends on two simple properties of the immediate snapshot executions, a subset of all possible executions, and on the well known graph theory result stating that every graph has an even number of vertices with odd degree (the handshaking lemma).